Compressible Multi-Phase Flow at Extreme Ambient Conditions

**Principal Investigator:**

Claus-Dieter Munz

**Affiliation:**

Institute of Aerodynamics and Gas Dynamics, University of Stuttgart

**Local Project ID:**

hpcmphas

**HPC Platform used:**

Hazel Hen and Hawk of HLRS

**Date published:**

Jet engines, combustion chambers and rocket engines are engineering applications, in which multi-phase flow occurs at extreme ambient conditions. Validated against experimental data, numerical simulations can also be applied to problems, which are expensive or not even accessible by experiments. In comparison to conventional simulation of fluid flows, multi-phase methods face major challenges. The behavior of the different materials and their interaction have to be modeled and solved accurately. Thereby, complex processes, such as real gas effects, the mixing of multiple materials and phase boundaries, occur. At high temperatures and pressures, an additional challenge is the compressibility of the fluids, which strongly couples thermodynamics and hydrodynamics and complicates the mathematical models and numerical methods. Therefore, compressible multi-phase flow simulations are computationally expensive and in need of high-performance computing (HPC) systems.

In this project, the compressible multi-phase flow solver FS3D.comp is developed. It focuses on two major applications: The investigation of droplet dynamics as well as trans- and supercritical jet simulations. Two different mathematical models are considered, the sharp interface method and the diffuse interface method. Both methods are incorporated into the FLEXI framework, which is a high order flow solver that is based on the Discontinuous Galerkin (DG) method with the option to switch to finite-volume sub-cells inside the DG cell for stabilization. FS3D.comp is developed by the Numerical Research Group of Prof. Munz at the Institute of Aerodynamics and Gas Dynamics at the University of Stuttgart. The method is very efficient on large scale state of the art CPU architectures. The description of liquids and gaseous phases requires the use of real gas Equations of State. Since their evaluation is computationally expensive, a tabulation technique was developed [4] and enhanced with a shared-memory technique in order to reduce the storage demand on HPC systems [3].

The sharp-interface method in FS3D.comp allows the simulation of pressure- and temperature-driven phase transition in thermodynamic non-equilibrium [2,5]. In addition, surface tension driven droplet-motion, e.g. colliding droplets and complex shock-droplet interactions, are also possible [7]. An example of a two-dimensional shock-droplet interaction is shown in Fig. 1. Shocks are flow phenomena, in which a sudden change in velocity, pressure and density occurs. The interaction of a liquid drop with a shock in a gaseous atmosphere results in a very complex flow field and different droplet break-up regimes can be observed. In Fig. 1 a shock-droplet interaction with a high surface-tension force is shown. Thus, the droplet is only slightly deformed. These investigations require very high spatial resolution, causing a high computational effort which is further increased if three-dimensional settings are considered.

Even with the resources of supercomputing centers like the HLRS the simulation of large-scale phenomena containing multiple phases, multiple species, compressibility effects and phase-transition, may still be not feasible with a detailed sharp-interface approach. Therefore, at high pressures and nearly critical temperature conditions a diffuse interface approach is also under development. This approach assumes that phase transitions occur in thermodynamic equilibrium only. The modeling effort, the numerical treatment, and the computational demands for such a simulation are still challenging. An example of such a large-scale phenomenon is shown in Fig. 2. A liquid fuel (n-Hexane) jet is injected in a combustion chamber filled with gas (Nitrogen). The break-up of the jet results in complex turbulent structures, which cause a mixing of the different species. We want to point out that the accurate capturing of mixing processes in a multi-phase real gas context requires well-resolved phase interfaces. Due to the significant computational effort such problems need high performance computing.

Although FS3D.comp has achieved many capabilities so far, further developments are necessary in the future. For non-equilibrium phase-transition in the sharp-interface method, further validation is required in order to assess the thermodynamic coupling of the two phases. Also, an extension of the current sharp-interface method to viscous flow simulations is planned so that a larger variety of flow simulations is possible. A comparison between the currently implemented approaches with alternative modeling strategies is in preparation. Therefore, two additional methods based on the hyperbolic Peshkov-Romenski equations [1] and the Navier-Stokes-Korteweg equations [6] are being implemented. In addition, further improvements concerning efficiency are planned in order to allow larger and more complex simulations of multi-phase flows.

**Research Team**

F. Fechter, F. Föll, T. Hitz, S. Jöns, J. Keim, C. Müller

**References**

[1] M. Dumbser, I. Peshkov, E. Romenski, and O. Zanotti, “High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids,” J. Comput. Phys., vol. 314, pp. 824–862, 2016.

[2] S. Fechter, C. D. Munz, C. Rohde, and C. Zeiler, “A sharp interface method for compressible liquid–vapor flow with phase transition and surface tension,” J. Comput. Phys., vol. 336, pp. 347–374, 2017.

[3] F. Föll, T. Hitz, J. Keim, and C.-D. Munz: Towards high-fidelity multiphase simulations: On the use of modern data structures on high performance computers, In: E. Nagel, H. Kröner, M. Resch (eds.): High-Performance Computing in Science and Engineering 2019, Springer

[4] F. Föll, T. Hitz, C. Müller, C. D. Munz, and M. Dumbser, “On the use of tabulated equations of state for multi-phase simulations in the homogeneous equilibrium limit,” Shock Waves, vol. 29, no. 5, pp. 769–793, 2019.

[5] T. Hitz, S. Joens, M. Heinen, J. Vrabec, and C.-D. Munz, “Comparison of Macro- and Microscopic Solutions of the Riemann Problem II. Two-Phase Shock Tube,” arXiv.org, 2020.

[6] T. Hitz, J. Keim, C.-D. Munz, and C. Rohde, “A parabolic relaxation model for the Navier-Stokes-Korteweg equations,” J. Comput. Phys., p. 109714, Jul. 2020.

[7] Müller C., Hitz T., Jöns S., Zeifang J., Chiocchetti S., Munz CD. (2020) Improvement of the Level-Set Ghost-Fluid Method for the Compressible Euler Equations. In: Lamanna G., Tonini S., Cossali G., Weigand B. (eds) Droplet Interactions and Spray Processes. Fluid Mechanics and Its Applications, vol 121. Springer, Cham

**Scientific Contact**

Prof. Dr. rer. nat. Claus-Dieter Munz

Institute of Aerodynamics and Gas Dynamics (IAG)

University of Stuttgart

Pfaffenwaldring 21, D-70569 Stuttgart (Germany)

e-mail: munz[@]iag.uni-stuttgart.de

*HLRS project ID: hpcmphas *

*August 2020*